I just saw a post saying NASA had calculated the universe to one hydrogen atom using 40 digits of Pi, I’m aware Pi is a very important number but how does it help us to work out distances etc?
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That piece of trivia (it takes only a certain amount of digits of pi to calculate the circumference of the universe to within the diameter of a hydrogen atom) is all about how many significant figures are actually important, and why memorizing a huge amount of pi is largely pointless, and less about what pi or the circumference of the universe actually are.
The specific amount is calculated by estimating the diameter of the observed universe (which is figured out based on the age of the oldest sources of light we can see and comparing that to the speed of light), and then taking that estimated number and using it to calculate the circumference (diameter * pi) with only the first 37 digits and comparing that to the same calculation but using the first 38 digits. The difference between the two numbers is a specific value. Both calculations give a number greater than 10^(24)m, but the difference between them is less than 5*10^(-11)m, or the radius of a hydrogen atom.
Which kind of makes sense, because 24 (the magnitude of the size of the observable universe) – -11(the magnitude of the size of a hydrogen atom) is 35, which is pretty close to the amount of decimals it takes to make adding more decimals redundant to real life sizes. The difference can be explained by the fact that we are using estimates, which will often add a magnitude of uncertainty or two.
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